What would you call this genre of music?

Other than the "Sweet Violets" genre, that is:
 
"There once was a farmer who took a young miss
In back of the barn where he gave her a...
Lecture on horses and chickens and eggs
And told her that she had such beautiful...
Manners that suited a girl of her charms
A girl that he wanted to take in his...
Washing and ironing and then if she did
They would get married and raise lots of...
 Sweet violets, sweeter than all the roses
 Covered all over from head to toe
 Covered all over with sweet violets."

Does anybody but me remember the kids' songs in this genre?  "Suzy Had a Steamboat" is the one that other people seem to know. But my favorite is this one, which I actually learned in junior high from another kid. What I love about it is that it sounds like it's from the 1890's (birch beer?  Anti-Irish prejudice?) but was still being passed from kid to kid in the early 60's. The tune is reminiscent of "Suzy had a Steamboat" but definitely not the same.

"Two Irishmen, two Irishmen were digging in a ditch.
One called the other a dirty son of a ...
Birch beer, birch beer, ten cents a glass,
If you do not like it, shove it up your...
Ask me no questions and you will get no answers,
If you do not like it, you can go to...
Hello, operator, give me number nine.
If you cannot reach it, please return my dime."